The quota function has not been intended for that kind of use, but should work.
Just run the questionnaire a few times and check the counts in the quota element. If it counts up, it has worked. Also mind not to forget the panel redirect element so that the quota stop will have an effect.
If course, you can also set the quota limits to 2 in order to give it a test.
However, I still think that that 5 lines of the second solution are way more simple.